Final answer:
The diameter of the bubble just as it reaches the surface of the lake at 20∘C can be found using the formula d2 = d1 * ∛(T2 / T1), where d1 is the initial diameter, d2 is the final diameter, T1 is the initial temperature, and T2 is the final temperature. Plugging in the values, we find that the bubble's diameter at the surface is approximately 1.414 cm.
Step-by-step explanation:
When an air bubble rises from the bottom to the top of a freshwater lake, its volume increases by 80% due to the decrease in pressure as it reaches the surface. In this case, the bubble's diameter increases as it rises to the surface where the water temperature is 20∘C compared to its starting diameter of 1.0 cm at 10∘C.
To calculate the bubble's diameter at the surface, we can use the formula:
d2 = d1 * ∛(T2 / T1)
Where d1 is the initial diameter, d2 is the final diameter, T1 is the initial temperature, and T2 is the final temperature.
Plugging in the values, we get:
d2 = 1.0 cm * ∛(20°C / 10°C)
d2 = 1.0 cm * ∛(2)
d2 = 1.0 cm * 1.414
d2 ≈ 1.414 cm